• Invariant differential operators in general position. (Russian) Funktsional. Anal. i Prilozhen. 16 (1982), no. 3, 86-87
• Characteristic classes of homogeneous foliations. (Russian) Uspekhi Mat. Nauk 39 (1984), no. 2(236), 189-190
• Characteristic classes of Grassmann foliations. (Russian) Funktsional. Anal. i Prilozhen. 19 (1985), no. 1, 83-84
• Characteristic classes of parabolic foliations and symmetric functions. Serdica, 11 (1985), 86-95
• Characteristic classes of parabolic foliations of series B, C, and D and degrees of isotropic Grassmannians. (Russian) Funktsional. Anal. i Prilozhen. 20 (1986), no. 2, 84-85
• An invariant of submanifolds transversal to a distribution. Russ. Math. Surv., 43, No 3 (1988), 193-194
• Calculation of the Bennequin invariant of a Legendrian curve by the geometry of its front. Func. Anal. Appl., 22, No 3 (1988), 89-90
• Characteristic classes of Lagrangian foliations. Func. Anal. Appl., 23, No 2 (1989), 90-91
• Around four vertices. Russ. Math. Surv., 45, No 1 (1990), 191-192
• Two remarks on the asymptotic Hopf invariant. Func. Anal. Appl., 24, No 1 (1990), 84-85
• Geometry of Lagrangian and Legendrian 2-webs. Diff. Geom. Appl., 3 (1993) 265--284
• Poncelet's theorem and dual billiards. L'Enseign. Math., 39 (1993), 189-194
• Outer billiards. Russ. Math. Surv., 48, No 6 (1993), 75-102
• Commuting dual billiard maps. Geom. Dedicata, 53 (1994), 57--68
• A cone eversion. Amer. Math. Monthly, 102 (1995), 52-56
• On the dual billiard problem. Adv. in Math. 115 (1995), 221-249
• The four vertex theorem revisited - two variations on the old theme. Amer. Math. Monthly, 102 (1995), 912-916
• Invariants of smooth triple point free plane curves. Knot Theory and Ramifications, 5 (1996), 531-552
• Asymptotic dynamics of the dual billiard transformation. J. Stat. Phys., 83 (1996), 27-38
• Projective connections, group Vey cocycle and deformation quantization. Int. Math. Research Notes. 1996, No 14, 705-722
• Sturm theory, Ghys theorem on zeroes of the Schwarzian derivative and flattening of Legendrian curves, with V. Ovsienko. Selecta Math. (NS), 2 (1996), 297-307
• On zeroes of the Schwarzian derivative. Topics in singularity theory, 229-239, AMS Transl., ser. 2, v. 180, 1997
• Introducing projective billiards. Ergod. Theory and Dynam. Syst., 17 (1997), 957-976
• Exact transverse line fields and projective billiards in a ball. Geom. and Funct. Anal., 7 (1997), 594-608
• Parameterized curves, Minkowski caustics, Minkowski vertices and conservative line fields. L'Enseign. Math., 43 (1997), 3-26
• Invariants of Legendrian and transverse knots in the standard contact space, with D. Fuchs. Topology 36 (1997), 1025-1053
• Estimates for the Bennequin number of Legendrian links from state models for knot polynomials. Math. Research Lett., 4 (1997), 143--156
• On functions with zero mean over a finite group. Func. Anal. Appl., 31, No 1 (1997), 93-94
• Fagnano orbits of polygonal dual billiards. Geom. Dedicata, 77 (1999), 279-286
• Geometry of exact transverse line fields and projective billiards. Differential and symplectic topology of knots and curves, 131-152, AMS Transl., ser. 2, v. 190, 1999
• Remarks on the geometry of exact transverse line fields. Differential topology, infinite-dimensional Lie algebras and applications, 247-260, AMS Transl., ser. 2, v. 194, 1999
• Projectively equivalent metrics, exact transverse line fields and the geodesic flow on the ellipsoid. Comm. Math. Helv., 74 (1999), 306-321
• More on paper folding, with D. Fuchs. Amer. Math. Monthly, 106 (1999), 27-35
• Going in circles: variations on the Money-Coutts theorem. Geom. Dedicata, 80 (2000), 201-209
• A four vertex theorem for polygons. Amer. Math. Monthly, 107 (2000), 830-833
• Outer billiards (in Russian). Math. Prosveshenie, ser.3, No 5 (2001), 125-135
• Projective geometry of polygons and discrete 4-vertex and 6-vertex theorems, with V. Ovsienko. L'Enseign. Math., 47 (2001), 3-19
• Topology of cyclic configuration spaces and periodic orbits of multi-dimensional billiards, with M. Farber. Topology, 41 (2002), 553-589
• Periodic trajectories in 3-dimensional convex billiards, with M. Farber. Manuscripta Math., 108, (2002), 431-437
• Billiards in Finsler and Minkowski geometries, with E. Gutkin. J. Geom. and Phys., 40 (2002), 277-301
• Ellipsoids, complete integrability and hyperbolic geometry. Moscow Math. J., 2 (2002), 185-198
• Dual billiards in the hyperbolic plane. Nonlinearity, 15 (2002), 1051-1072
• Rational billiards and flat structures, with H. Masur. Handbook of Dynamical Systems, v. 1A, North-Holland, 2002, 1015--1089
• On skew loops, skew branes and quadratic hypersurfaces. Moscow Math. J., 3 (2003), 681-690
• On polygonal dual billiard in the hyperbolic plane, with F. Dogru. Reg. Chaotic Dynamics, 8 (2003), 67-82
• A tale of a geometric inequality. MASS Selecta, AMS, 2003, 257-262
• Topological robotics: motion planning in projective spaces, with M. Farber and S. Yuzvinsky. Int. Math. Research Notes. 2003, No 34, 1853-1870
• On three-periodic trajectories of multi-dimensional dual billiards. Alg. Geom. Topology, 3 (2003), 993-1004
• Remarks on magnetic flows and magnetic billiards, Finsler metrics and a magnetic analog of Hilbert's fourth problem. Dynamical systems and related topics, Cambridge Univ. Press, 2004, 233-252
• Dual billiards, with F. Dogru. Math. Intelligencer, 27, No 4 (2005), 18-25
• Tire track geometry: variations on a theme. Israel J. Math., 151 (2006), 1-28
• Non-existence of n-dimensional T-embedded discs in R^(2n), with G. Stojanovic . Comm. Math. Helv., 81 (2006), 877-882
• Complexity of piecewise convex transformations in two dimensions, with applications to polygonal billiards on surfaces of constant curvature, with E. Gutkin. Moscow Math. J., 6 (2006), 673-701
• On configuration spaces of plane polygons, sub-Riemannian geometry and periodic orbits of outer billiards, with D. Genin. Journal of Modern Dynamics 1 (2007), 155-173
• Book review of Arnold's Problems. Math. Intelligencer, 29, No 1 (2007), 49-52
• The Poncelet grid and the billiard in an ellipse, with M. Levi. Amer. Math. Monthly, 114 (2007), 895-908
• Hyperbolic Caratheodory conjecture, with V. Ovsienko. Proc. of Steklov Inst., 258 (2007), 178-193
• Geodesics on an ellipsoid in Minkowski space, with D. Genin and B. Khesin. L'Enseign. Math., 53 (2007), 307-331
• A proof of Culter's theorem on the existence of periodic orbits in polygonal outer billiards. Geom. Dedicata, 129 (2007), 83-87
• Totally skew embeddings of manifolds, with M. Ghomi. Math. Z., 258 (2008), 499-512
• On algebraically integrable outer billiards. Pacific J. Math., 235 (2008), 89-92
• Converse Sturm-Hurwitz-Kellogg theorem and related results. J. Fixed Point Theory Appl., 3 (2008), 121-130
• Birkhoff billiards are insecure. Discr. Cont. Dyn. Syst., 23 (2009), 1035-1040
• What is ... the Schwarzian derivative? with V. Ovsienko. Notices of AMS, 56 (2009), 34-36
• Quasiperiodic motion for the Pentagram Map, with V. Ovsienko and R. Schwartz. Electron. Res. Announc. Math. Sci., 16 (2009), 1-8
• Spaces of pseudo-Riemannian geodesics and pseudo-Euclidean billiards, with B. Khesin. Adv. Math., 221 (2009), 1364-1396
• Self-dual polygons and self-dual curves, with D. Fuchs. Funct. Anal. and Other Math., 2 (2009), 203-220
• On bicycle tire tracks geometry, hatchet planimeter, Menzin's conjecture and oscillation of unicycle tracks, with M. Levi. Experimental Math., 18 (2009), 173-186
• Sylvester's problem (in Russian), with V. Timorin. Kvant 2009, No 5, 2-6, No 6, 6-10
• Existence and non-existence of skew branes. J. Fixed Point Theory Appl., 7 (2010), 419-431
• Variations on the Tait-Kneser theorem, with V. Timorin. Preprint
• The Pentagram map: a discrete integrable system, with V. Ovsienko and R. Schwartz. Comm. Math. Phys., 299 (2010), 409-446
• Topological aspects of the Dvoretzky Theorem, with D. Burago and S. Ivanov. J. Topology and Analysis, 2 (2010), 453-467
• Contact complete integrability, with B. Khesin. Reg. Chaotic Dynamics, 15 (2010), 504-520
• Elementary surprises in projective geometry, with R. Schwartz. Math. Intelligencer, 32 (2010) No 3, 31-34
• Periodic trajectories in the regular pentagon, with D. Davis and D. Fuchs. Moscow Math. J., 11 (2011), 1-23
• The pentagram integrals on inscribed polygons, with R. Schwartz. Electr. J. Comb., 18 (2011), P171
• Variations on R. Schwartz's inequality for the Schwarzian derivative. Discr. Comp. Geom., 46 (2011), 724-742
• 2-frieze patterns and the cluster structure of the space of polygons, with S. Morier-Genoud and V. Ovsienko. Ann. Inst. Fourier, 62 (2012), 937-987
• The (un)equal tangents problem. Amer. Math. Monthly, 119 (2012), 398-405
• Higher pentagram maps, weighted directed networks, and cluster dynamics, with M. Gekhtman, M. Shapiro and V. Vainshtein. Electron. Res. Announc. Math. Sci., 19 (2012), 1-17
• Liouville-Arnold integrability of the pentagram map on closed polygons, with V. Ovsienko and R. Schwartz. Duke Math. J., 162 (2013), 2149-2196
• Periodic trajectories in the regular pentagon, II, with D. Fuchs. Moscow Math. J., 13 (2013), 19-32
• On fibrations with flat fibers, with V. Ovsienko. Bull. London Math. Soc., 45 (2013), 625-632
• The equal tangents property, with J. Jeronimo-Castro and G. Ruiz-Hernandez. Adv. Geom., 14 (2014), 447-453
• Tractrices, bicycle tire tracks, hatchet planimeters, and a 100-year-old conjecture, with R. Foote and M. Levi. Amer. Math. Monthly, 120 (2013), 199-216
• Osculating curves: around the Tait-Kneser Theorem, with E. Ghys and V. Timorin. Math. Intelligencer, 35, No 1 (2013), 61-66
• On the discrete bicycle transformation, with E. Tsukerman. Publ. Math. Uruguay (proc. of the Montevideo Dynamical Systems Congress 2012), 14 (2013), 201-220
• Dragon curves revisited. Math. Intelligencer, 36, No 1 (2014), 13-17
• Proofs (not) from The Book. Math. Intelligencer, 36, No 2 (2014), 9-14
• Circumcenter of Mass and generalized Euler line, with E. Tsukerman. Discr. Comp. Geom., 51 (2014), 815-836
• Linear difference equations, frieze patterns and combinatorial Gale transform, with S. Morier-Genoud, V. Ovsienko and R. Schwartz. Forum of Mathematics, Sigma, 2 (2014), e22
• On curves and polygons with the equiangular chord property, with T. Aougab, X. Sun and Y. Wang. Pacific J. Math., 274 (2015), 305-324
• Coxeter's frieze patterns and discretization of the Virasoro orbit, with V. Ovsienko. J. Geom. and Phys., 87 (2015), 373-381
• SL 2 (Z)-tiling of the torus, Coxeter-Conway friezes and Farey triangulations, with S. Morier-Genoud and V. Ovsienko. L'Enseign. Math., 61 (2015), 71-92
• A Baker's dozen of problems. Arnold Math. J., 1 (2015), 59-67
• Remarks on the circumcenter of mass, with E. Tsukerman. Arnold Math. J., 1 (2015), 101-112
• Introducing supersymmetric frieze patterns and linear difference operators, with S. Morier-Genoud and V. Ovsienko. Math. Zeitschrift, 281 (2015), 1061-1087
• Configuration spaces of plane polygons and a sub-Riemannian approach to the equitangent problem, with J. Jeronimo-Castro. J. Dyn. Control Syst., 22 (2016), 227-250
• The Six Circles Theorem revisited, with D. Ivanov. Amer. Math. Monthly, 123 (2016), 689-698
• Integrable cluster dynamics of directed networks and pentagram maps, with M. Gekhtman, M. Shapiro and V. Vainshtein. Adv. in Math., 300 (2016), 390-450
• On Lagrangian tangent sweeps and Lagrangian outer billiards, with D. Fuchs. Geom. Dedicata, 182 (2016), 203-213
• Skewers. Arnold Math. J., 2 (2016), 171-193
• Centers of mass of Poncelet polygons, 200 years after, with R. Schwartz. Math. Intelligencer, v. 38, No 2 (2016), 29-34
• Hopf fibrations and Hurwitz-Radon numbers, with V. Ovsienko. Math. Intelligencer, v. 38, No 4 (2016), 11-18
• Polynomials as polygons. Math. Intelligencer, v. 39, No 1 (2017), 41-43
• On the bicycle transformation and the filament equation: results and conjectures. J. Geom. and Phys., 115 (2017), 116-123
• Billiard transformations of parallel flows: a periscope theorem, with A. Plakhov and D. Treschev. J. Geom. and Phys., 115 (2017), 157-166
• Iterating evolutes and involutes, with M. Arnold, D. Fuchs, I. Izmestiev, and E. Tsukerman. Discr. Comp. Geom., 58 (2017), 80-143
• Ivory's Theorem revisited, with I. Izmestiev. J. Integrable Systems, 2 (2017), 1-36
• Iterating evolutes of spatial polygons and of spatial curves, with D. Fuchs. Moscow Math. J., 17 (2017), 667-689
• Vladimir Igorevich Arnold, with B. Khesin. Biogr. Mems Fell. Royal Soc., publ. online 08/30/17
• Dual numbers, weighted quivers, and extended Somos and Gale-Robinson sequences, with V. Ovsienko. Algebras Represent. Theory, 21 (2018), 1119-1132
• Introducing symplectic billiards, with P. Albers. Advances in Math., 333 (2018), 822-867
• Book review of "A singular mathematical promenade" by E. Ghys Math. Intelligencer, v. 40, No 2 (2018), 85-88
• A four vertex theorem for frieze patterns? Math. Intelligencer, v. 40, No 4 (2018), 14-18
• Open problems, questions, and challenges in finite-dimensional integrable systems, with A. Bolsinov, V. Matveev, and E. Miranda. Philosoph. Trans. Royal Society A, 376 (2018), 20170430 (40 pp)
• On centro-affine curves and Backlund transformations of the KdV equation. Arnold Math. J., 4 (2018), 445-458
• Projective configuration theorems: old wine into new wineskins. in Geometry in History, Springer, 2019, 401--434
• Kasner meets Poncelet. Math. Intelligencer, v. 41, No 4 (2019), 56-59
• Fun problems in geometry and beyond, with B. Khesin. SIGMA 15 (2019), 097, 21 pages
• Tire tracks and integrable curve evolution, with G. Bor, M. Levi, and R. Perline. Int. Math. Res. Notes, 2020, no. 9, 2698-2768.
• Descartes circle theorem, Steiner porism, and spherical designs, with R. Schwartz. Amer. Math. Monthly, v. 127 (2020), 238-248
• Book review of "The Scottish Book. Mathematics from the Scottish Cafe" . Math. Intelligencer, v. 42, No1 (2020), 71-74
• Counting periodic trajectories of Finsler billiards, with P. Blagojevic, M. Harrison, and G. Ziegler. SIGMA 16 (2020), 022, 33 pages
• Wire billiards, the first steps, with M. Bialy and A. Mironov. Advances in Math., 368 (2020), 107154, 27 pp.
• Two variations on the periscope theorem. Reg. Chaotic Dynamics, 25 (2020), 11-17
• Book review of "You Failed Your Math Test, Comrade Einstein". Math. Intelligencer, v. 42, No 3 (2020), 83-87
• Four equivalent properties of integrable billiards, with A. Glutsyuk and I. Izmestiev. Israel J. Math., 241 (2021), 693-719
• Polygonal symplectic billiards, with P. Albers, G. Banhatti, F. Sadlo, and R. Schwartz. Preprint
• Billiards in ellipses revisited, with A. Akopyan and R. Schwartz. European J. Math., online first
• Dan Reznik's identities and more, with M. Bialy. European J. Math., online first
• Remarks on Joachimsthal integral and Poritsky property, with M. Arnold. Arnold Math. J., 7 (2021), 483-491
• Polar bear or penguin? Musings on Earth cartography and Chebyshev nets, with B. Khesin. Math. Intelligencer, v. 43, No 1 (2021), 20-24
• Cross-ratio dynamics on ideal polygons, with M. Arnold, D. Fuchs, and I. Izmestiev. Int. Math. Res. Notes, 2022, no. 9, 6770-6853
• Symplectically convex and symplectically star-shaped curves - a variational problem, with P. Albers. J. Fixed Point Theory Appl. (Viterbo Festschrift), 24 (2022), no. 2, Paper No. 27, 24 pp.
• Variations on the Tait-Kneser theorem, with G. Bor and C. Jackman. Math. Intelligencer, v. 43, No 3 (2021), 8-14
• Loewner's "forgotten" theorem, with P. Albers. Math. Intelligencer, v. 44, No 1 (2022), 7-11
• Remarks on rigidity properties of conics. Reg. Chaotic Dynamics, 27 (2022), 18-23
• Open problems on billiards and geometric optics, with M. Bialy, C, Fierobe, A. Glutsyuk, M. Levi, and A. Plakhov. Arnold Math. J., 8 (2022), 411-422
• On cusps of caustics by reflection: a billiard variation on Jacobi's Last Geometric Statement, with G. Bor. Amer. Math. Monthly, to appear
• Self-Backlund curves in centroaffine geometry and Lame's equation, with M. Bialy and G. Bor. Communication of AMS, 2 (2022), 232-282
• A family of integrable transformations of centroaffine polygons: geometrical aspects, with M. Arnold and D. Fuchs. Ann. Inst. Fourier, to appear
• On projective evolutes of polygons, with M. Arnold and R. Schwartz. Experimental Math., online first
• On conformal points of area preserving maps and related topics, with P. Albers. J. Geom. Physics, 180, Oct. 2022, 104644
• Bicycling geodesics are Kirchhoff rods, with G. Bor and C. Jackman. Preprint
• Differential geometry of space curves: forgotten chapters, with D. Fuchs, I. Izmestiev, M. Raffaelli, and G. Szewieczek. Preprint
• Iterating skew evolutes and skew involutes: a linear analog of the bicycle kinematics. Preprint